Gravitational Trapping Near Domain Walls and Stable Solitons

In this work, the behavior of test particles near a domain wall of a stable false vacuum bubble is studied. It is shown that matter is naturally trapped in the vicinity of a static domain wall, and also, that there is a discontinuity in the test particle's velocity when crossing the domain wall. The latter is unexpected as it stands in contrast to Newtonian theory, where infinite forces are not allowed. The weak field limit is defined in order to show that there is no conflict with the non-relativistic behavior of gravitational fields and particle motions under these conditions.